Color conversion circuit and method of color conversion using interpolation from conversion coefficients some of which are substituted

1. A color conversion circuit for converting input color data into output color data, the input color data being positioned within a three-dimensional color space, which is divided in a plurality of unit cubes having a fixed dimension, at a position specified by coordinates of the input color data, the conversion circuit comprising: a three-dimensional look-up table that stores conversion coefficients at respective vertexes of the plurality of unit cubes; a substitution circuit that reads conversion coefficients at vertexes of one of the unit cubes in which the input color data is positioned from the three-dimensional look-up table and performs a substitution of some of the conversion coefficients read from the look-up table with substitute conversion coefficients expressed by other ones of the conversion coefficients read from the look-up table; and an interpolation circuit that performs an interpolation from the conversion coefficients after the substitution to generate converted coordinates of the output color data using volumes of rectangular parallelepipeds that divide the one of the unit cubes such that each of the rectangular parallelepipeds shares the input color data as a vertex, wherein: each of the conversion coefficients at vertexes on either end of a diagonal line placed on a gray axis of the color space of each of the unit cubes on the gray axis has three components equal with each other, the vertexes of the each of the unit cubes on the gray axis include, in addition to the vertexes on the either end of the diagonal line, six other vertexes, and when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution circuit groups the six other vertexes in two groups depending on which of the vertexes on the either end of the diagonal line is closer, selects at least one of the vertexes from each of the two groups, and performs the substitution of the conversion coefficients at the selected vertexes such that a sum of the conversion coefficients after the substitution at the vertexes in each of the two groups is expressed by a linear combination of the conversion coefficients at the vertexes on either end of the diagonal line.

2. The color conversion circuit according to claim 1 , wherein, when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution circuit performs the substitution such that the sum of the conversion coefficients after the substitution at the vertexes in each of the two groups is equal to a sum of two times the conversion coefficient at a closer one of the vertexes and the conversion coefficient at a further one of the vertexes on the either end of the diagonal line.

3. The color conversion circuit according to claim 1 , wherein, when the one of the unit cubes has the diagonal, line placed on the gray axis, the substitution circuit selects one of the vertexes furthest from the input color data from each of the two groups, and performs the substitution of the conversion coefficients at the selected vertexes.

4. The color conversion circuit according to claim 1 ,wherein, when the one of the unit cubes has the diagonal, line placed on the gray axis, the substitution circuit selects at least one of the vertexes depending on in which of six tetrahedrons, which divide the one of the unit cubes such that each of the tetrahedrons shares the diagonal line of the one of the unit cubes as an edge, the input color data is positioned.

5. The color conversion circuit according to claim 4 , wherein: one of the six tetrahedrons in which the input color data is positioned has diagonal lines of two adjoining surfaces of the one of the unit cubes as two edges; and the substitution circuit selects vertexes on either end of a furthest edge of the one of the unit cubes furthest from an edge of the one of the unit cubes shared by the adjoining surfaces and substitutes the conversion coefficients at the selected vertexes.

6. A method of converting input color data into output color data, comprising: receiving input color data positioned in a three-dimensional color space, which is divided in a plurality of unit cubes having a fixed dimension, at a position specified by coordinates of the input color data; reading conversion coefficients at vertexes of one of the unit cubes in which the input color data is positioned; performing a substitution of some of the read conversion coefficients with substitute conversion coefficients expressed by other ones of the read conversion coefficients; and performing an interpolation from the conversion coefficients after the substitution to generate converted coordinates of the output color data using volumes of rectangular parallelepipeds that divide the one of the unit cubes such that each of the rectangular parallelepipeds shares the input color data as a vertex, wherein: each of the conversion coefficients at vertexes on either end of a diagonal line placed on a gray axis of the color space of each of the unit cubes on the gray axis has three components equal with each other, the vertexes of the each of the unit cubes on the gray axis include, in addition to the vertexes on the either end of the diagonal line, six other vertexes, and when the one of the unit cubes has the diagonal line placed on a on the gray axis, the substitution is performed by a substitution circuit to group the six other vertexes in two groups depending on which of the vertexes on the either end of the diagonal line is closer, select at least one of the vertexes from each of the two groups, and substitute the conversion coefficients at the selected vertexes such that a sum of the conversion coefficients after the substitution at the vertexes in each of the two groups is expressed by a linear combination of the conversion coefficients at the vertexes on the either end of the diagonal line.

7. The method according claim 6 , wherein, when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution is performed such that the sum of the conversion coefficients after the substitution at the vertexes in each of the two groups is equal to a sum of two times the conversion coefficient at a closer one of the vertexes and the conversion coefficient at a further one of the vertexes on the either end of the diagonal line.

8. The method according to claim 6 , wherein, when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution includes selecting one of the vertexes furthest from the input color data from each of the two groups so that the conversion coefficients at the selected vertexes are substituted.

9. The method according to claim 6 , wherein, the one of the unit cubes has the diagonal line placed on the gray axis; the substitution includes selecting the at least one of the vertexes depending on in which of six tetrahedrons, which divide the one of the unit cubes such that each of the tetrahedrons shares the diagonal line of the one of the unit cubes as an edge, the input color data is positioned.

10. The method according to claim 9 , wherein: one of the six tetrahedrons in which the input color data is positioned has diagonal lines of two adjoining surfaces of the one of the unit cubes as two edges; and the substitution includes selecting vertexes on either end of a furthest edge of the one of the unit cubes furthest from an edge of the one of the unit cubes shared by the adjoining surfaces so that the conversion coefficients at the selected vertexes are substituted.

11. A color conversion circuit for converting input color data into output color data, the input color data being positioned within a three-dimensional color space, which is divided in a plurality of unit cubes having a fixed dimension, at a position specified by coordinates of the input color data, the conversion circuit comprising: a three-dimensional look-up table that stores conversion coefficients of respective vertexes of the plurality of unit cubes; a substitution circuit that reads conversion coefficients at vertexes of one of the unit cubes in which the input color data is positioned from the three-dimensional look-up table and performs a substitution of some of the conversion coefficients read from the look-up table with substitute conversion coefficients expressed by other ones of the conversion coefficients read from the look-up table; and an interpolation circuit that performs an interpolation from the conversion coefficients after the substitution to generate converted coordinates of the output color data using volumes of rectangular parallelepipeds that divide the one of the unit cubes such that each of the rectangular parallelepipeds shares the input color data as a vertex, wherein: each of the conversion coefficients at vertexes on either end of a diagonal line placed on a gray axis of the color space of each of the unit cubes on the gray axis has three components equal with each other, the vertexes of the each of the unit cubes on the gray axis include, in addition to the vertexes on the either end of the diagonal line, six other vertexes, and when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution circuit groups the six other vertexes in two groups depending on which of the vertexes on the either end of the diagonal line is closer, selects at least one of the vertexes from each of the two groups, and performs the substitution of the conversion coefficients at the selected vertexes such that a sum of the conversion coefficients after the substitution at the vertexes in each of the two groups is equal to a sum of two times the conversion coefficient at a closer one of the vertexes and the conversion coefficient at a further one of the vertexes on the either end of the diagonal line.

12. The color conversion circuit according to claim 11 , wherein, when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution circuit selects one of the vertexes furthest from the input color data from each of the two groups and performs the substitution of the conversion coefficients at the selected vertexes.

13. The color conversion circuit according to claim 11 , wherein, when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution circuit selects the at least one of the vertexes depending on in which of six tetrahedrons, which divide the one of the unit cubes such that each of the tetrahedrons shares the diagonal line of the one of the unit cubes as an edge, the input color data is positioned.

14. The color conversion circuit according to claim 13 , wherein: one of the six tetrahedrons in which the input color data is positioned has diagonal lines of two adjoining surfaces of the one of the unit cubes as two edges; and the substitution circuit selects vertexes on either end of a furthest edge of the one of the unit cubes furthest from an edge of the one of the unit cubes shared by the adjoining surfaces and substitutes the conversion coefficients at the selected vertexes.

15. A method of converting input color data into output color data, comprising: receiving input color data positioned in a three-dimensional color space, which is divided in a plurality of unit cubes having a fixed dimension, at a position specified by coordinates of the input color data; reading conversion coefficients at vertexes of one of the unit cubes in which the input color data is positioned; performing a substitution of some of the read conversion coefficients with substitute conversion coefficients expressed by other ones of the read conversion coefficients; and performing an interpolation from the conversion coefficients after the substitution to generate converted coordinates of the output color data using volumes of rectangular parallelepipeds that divide the one of the unit cubes such that each of the rectangular parallelepipeds shares the input color data as a vertex, wherein: each of the conversion coefficients at vertexes on either end of a diagonal line placed on a gray axis of the color space of each of the unit cubes on the gray axis has three components equal with each other, the vertexes of the each of the unit cubes on the gray axis include, in addition to the vertexes on the either end of the diagonal line, six other vertexes, and when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution is performed by a substitution circuit to group the six other vertexes in two groups depending on which of the vertexes on the either end of the diagonal line is closer, select at least one of the vertexes from each of the two groups, and substitute the conversion coefficients at the selected vertexes such that a sum of the conversion coefficients aider the substitution at the vertexes in each of the two groups is equal to a sum of two times the conversion coefficient at a closer one of the vertexes and the conversion coefficient at a further one of the vertexes on the either end of the diagonal line.

16. The method according to claim 15 , wherein, when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution includes selecting one of the vertexes furthest from the input color data from each of the two groups so that the conversion coefficients at the selected vertexes are substituted.

17. The method according to claim 15 , wherein, when the one of the unit cubes has the diagonal line placed on the gray axis, the substitution includes selecting the at least one of the vertexes depending on in which of six tetrahedrons, which divide the one of the unit cubes such that each of the tetrahedrons shares the diagonal line of the one of the unit cubes as an edge, the input color data is positioned.

18. The method according to claim 17 , wherein: one of the six tetrahedrons in which the input color data is positioned has diagonal lines of two adjoining surfaces of the one of the unit cubes as two edges; and the substitution includes selecting vertexes on either end of a furthest edge of the one of the unit cubes furthest from an edge of the one of the unit cubes shared by the adjoining surfaces so that the conversion coefficients at the selected vertexes are substituted.